Persistent current in an almost staggered Harper model

•The persistent current for the Harper model is not metallic in the metallic regime.•This stems from the nature of central band states for the staggered case.•When the superlattice is not commensurate the persistent current is insulating.•Even in the metallic regime Harper model may exhibit insulating current.

In this paper we study the persistent current (PC) of a staggered Harper model, close to the half-filling. The Harper model is different than other one dimensional disordered systems which are always localized, since it is a quasi-periodic system with correlated disorder resulting in the fact that it can be in the metallic regime. Nevertheless, the PC for a wide range of parameters of the Harper model does not show typical metallic behavior, although the system is in the metallic regime. This is a result of the nature of the central band states, which are a hybridization of Gaussian states localized in superlattice points. When the superlattice is not commensurate with the system length, the PC behaves as an insulator. Thus even in the metallic regime a typical finite Harper model may exhibit a PC expected from an insulator.